پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 642 |
| تعداد مقالات | 9,410 |
| تعداد مشاهده مقاله | 68,134,827 |
| تعداد دریافت فایل اصل مقاله | 39,841,322 |
Wavelet frames associated with linear canonical transform on spectrum | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 186، دوره 13، شماره 2، مهر 2022، صفحه 2297-2310 اصل مقاله (436.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22872.2426 | ||
| نویسندگان | ||
| Mohd Younus Bhat* ؛ Aamir Hamid Dar | ||
| Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India | ||
| تاریخ دریافت: 20 اسفند 1399، تاریخ بازنگری: 14 خرداد 1400، تاریخ پذیرش: 22 خرداد 1400 | ||
| چکیده | ||
| The linear canonical transform (LCT) provides a unified treatment of the generalized Fourier transforms in the sense that it is an embodiment of several well-known integral transforms including the Fourier transform, fractional Fourier transform, Fresnel transform. Using this fascinating property of LCT, we in this paper construct associated wavelet frames. To be precise we introduce wavelet frames whose construction depends on the nonuniform multiresolution analysis associated with linear canonical transform(LCT-NUMRA) whose translation set is not necessarily a group. The translation set is taken for elements in $\Lambda=\left\{ 0,r/N\right\}+2\,\mathbb Z,\mathbb N\ge 1$ (an integer) and r is an odd integer with $1\le r\le 2N-1$ such that r and N are relatively prime and ${\mathbb Z}$ is the set of all integers. Furthermore, we establish a necessary and sufficient conditions for such nonuniform wavelet frames associated with linear canonical transform. | ||
| کلیدواژه‌ها | ||
| Frame؛ nonuniform LCT wavelets؛ wavelet frame؛ Linear canonical transform | ||
| مراجع | ||
|
[1] M.Y. Bhat and A.H. Dar, Wavelet packets associated with linear canonical transform on spectrum, Int. J. Wavelets Multiresolution Inf. Process 6 (2021), 2150030[2] M.Y. Bhat and A.H. Dar, Vector-valued nonuniform multiresolution analysis associated with linear canonical transform, preprint, 2020. [3] M.Y. Bhat and A.H. Dar, Octonion spectrum of 3D short-time LCT signals, Optik 261 (2022), 169156 [4] M.Y. Bhat and A.H. Dar, Quadratic-phase wave packet transform, Optik 261 (2022), 169120 [5] M.Y. Bhat and A.H. Dar, Scaled Wigner distribution in the offset linear canonical domain, Optik 262 (2022), 169286. [6] M.Y. Bhat and A.H. Dar, Multiresolution analysis for linear canonical S transform, Adv. Oper. Theory 68 (2021), 1–11. [7] M.Y. Bhat and A.H. Dar, Fractional vector-valued nonuniform MRA and associated wavelet packets on L 2 (R, CM), Fractional Calculus Appl. Anal. 25 (2022), 687–719. [8] M.Y. Bhat and A.H Dar, Convolution and correlation theorems for Wigner–Ville distribution associated with the quaternion offset linear canonical transform, Signal Image Video Process. 16 (2022), 1235-–1242 [9] A. Bultheel and H. Martınez-Sulbaran, Recent developments in the theory of the fractional Fourier and linear canonical transforms, Bull. Belg. Math. Soc. 13(2006), 971–1005 [10] I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmonic Anal. 14 (2003), 1–46. [11] E. Hernadez and G. Weiss, A first course on wavelets, CRC Press, 1996. [12] R.J. Duffin and A.C. Shaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366. [13] J.P. Gabardo and M.Z. Nashed, Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998), 209–241. [14] J.P. Gabardo and X. Yu, Wavelets associated with nonuniform multiresolution analysis and one-dimensional spectral pairs, J. Math. Anal. Appl. 323 (2006), 798–817. [15] B. Han, Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix, J. Comput. Appl. Math. 155 (2003), 43–67. [16] J.J. Healy, M.A. Kutay, H.M. Ozaktas and J.T. Sheridan, Linear canonical transforms, New York, Springer, 2016. [17] J. Krommweh, Tight frame characterization of multiwavelet vector functions in terms of the polyphase matrix, Int. J. Wavelets Multiresolution Inf. Process. 7 (2009), 9–21. [18] M. Moshinsky and C. Quesne, Linear canonical transformations and their unitary representations, J. Math. Phys. 12 (1971), no. 8, 1772–1780 [19] J. Pan and J. Wang, Texture segmentation using separable and non-separable wavelet frames, IEEE Trans. Fund. Electron. Commun. Comput. Sci. 82 (1999), no. 8, 1463–1474. [20] F. A. Shah and Waseem, Nonuniform multiresolution analysis associated with linear canonical transform, J. Pseudo-Differ. Oper. Appl. 21 (2021), no. 1, 1–35. [21] F.A. Shah and M.Y. Bhat, Vector-valued nonuniform multiresolution analysis on local fields, Int. J. Wavelets Multiresolution Inf Process 13 (2015), no. 4, 1550029. [22] F.A. Shah, Inequalities for nonuniform wavelet frames, Georgian Math. J. 28 (20211), no. 1, 149–156. [23] J. Shim, X. Lium and N. Zhang, Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform, Signal Image Video Process. 9 (2015), no. 1, 211–220. [24] V. Sharma and P. Manchanda, Nonuniform wavelet frames in L 2 (R), Asian-Eur. J. Math. 8 (2015), no. 2, Article ID: 1550034. [25] T.Z. Xu and B.Z. Li, Linear canonical transform and its applications, Science Press, Beijing, China, 2013. | ||
|
آمار تعداد مشاهده مقاله: 43,662 تعداد دریافت فایل اصل مقاله: 29,900 |
||